Geophysics and planetary science
Mathematics plays an important role in our understanding of the processes that shape our Earth and other planets.
Researchers in the Department of Mathematics are at the forefront of a wide range of research in geophysics, from predicting the behaviour of snow avalanches and the transport of volcanic ash in the atmosphere to remote sensing and characterisation of hydrocarbon reservoirs.
Much of this research uses mathematical ideas in Continuum Mechanics to understand interactions and flows of rock, ice, water and air in the environment. These problems frequently span large spatial and temporal ranges, and identifying dominant causal mechanisms is often a challenging process. At large scales, many of these problems are dominated by background rotation (associated with planetary rotation) and/or stratification (associated with non-uniform distributions of heat/solute/pollutant).
Volcanoes form a natural laboratory for a wide range of fluid and granular processes. A volcanic eruption may inject large quantities of fine ash several kilometres into the atmosphere, where it poses a significant hazard to aviation. Researchers in the Department of Mathematics model the dispersal of this ash, in particular how it is influenced by the spreading 'umbrella cloud' that forms above a large eruption. This modelling aims to improve the accuracy of volcanic ash forecasts, and has close links with the remote sensing of volcanic plumes undertaken in the Department of Earth and Environmental Science.
Erupted material is also carried down the flanks of a volcano by pyroclastic density currents and debris flows. The Department of Mathematics is at the forefront of modelling the processes of erosion, deposition and grain-size segregation that increase the maximum depth and the run-out distance of these these hazardous geophysical mass flows. Through analysis of the underlying mathematics, insights from these volcanic flows have applied to a diverse range of other geophysical flows, such as snow avalanches and dry granular flows on the moon. For further details, see our research on granular materials.
This work is essentially interdisciplinary in nature, combining insights from theory, experiment and observations. A recent project led by researchers in the Department of Mathematics has combined mathematical modelling with fieldwork to explain why iron-based meteorites are rarely found in otherwise meteorite-rich areas of Antarctica.
The mathematics of Inverse Problems also has widespread applications in geophysics, such as geophysical tomography, reservoir characterization, and remote sensing. Current research projects in the Department of Mathematics include, large scale electromagnetic inverse problems with geophysical applications, history matching and data assimilation for the characterization of hydrocarbon reservoirs, seismic full waveform inversion and gravity and gradiometry imaging.
More information about our research, and some papers, can be found by browsing the webpages of academic staff members. Potential PhD students may email staff directly to discuss possible projects.